1. Field of the Invention
The present invention relates to a method for process simulation in which a fabrication process of a device such as a semiconductor integrated circuit is simulated, and more specifically to a method for process simulation capable of simulating segregation phenomena of any impurities with high accuracy.
2. Description of the Related Art
Process simulation represented by simulation of fabrication of semiconductor devices uses a computer to numerically analyze processes such as an ion implantation process and diffusion process without actual fabrication of the devices, and estimates physical quantities and the shape such as an impurity profile in the devices. Since upon the process simulation for impurity diffusion it is difficult to analytically solve a diffusion equation, it is general to prepare a proper device model, and divide the device model to two-dimensional and three-dimensional meshes to perform discrete numerical calculation of changes in physical quantities at mesh points using a finite element method or the like.
As the shape of the mesh there are frequently used triangles in the case of the two-dimensional simulation and tetrahedrons in the case of the three-dimensional simulation. In these cases, in order to achieve the appropriate process simulation, it is essential for circumcenters of adjacent triangles (tetrahedrons) not to mutually intersect. For this, there may be provided Delaunay partition: there is no vertex of another triangle (tetrahedron) in a circumscribed circle (sphere) of each triangle (tetrahedron) constituting the mesh.
In a device which is an object of the process simulation there is a portion which forms a boundary or interface between two substance regions that make contact with each other. The two substance regions are, for example, a silicon layer and an oxide layer, respectively. Since the boundary is a plane of discontinuity, mere disposition of mesh points on the boundary makes simulation of the diffusion phenomenon difficult. In contrast, the boundary is an area where segregation is liable to occur as an actual physical phenomenon. The boundary is also an area in which accurate simulation is desired for investigating the segregation phenomenon.
Conventionally, one of the following methods is used for improving accuracy of the simulation: (1) a method of treating each mesh point on the boundary as a duplicated point (i.e., double point) (J. Electrochem. Soc., Vol. 126, No. 11, pp. 1939-1945, 1979, or process simulation program xe2x80x9cTSUPREM4xe2x80x9d), (2) a method of treating each mesh point on the boundary as a duplicated point and disposing a boundary protective layer (Syo, Kumashiro, SISPAD ""96, PP. 173-174, 1996, or Singakugiho (Technical Report of the Institute of Electronics, Information and Communication Engineers), Vol. 96, No. 258, pp.31-37, 1996), and (3) a method of treating each mesh point on the boundary as a triplicated point (i.e., triple point) (Singakugiho, Vol. 97., No. 268, pp. 1-8, 1997).
In the following, such conventional methods will be described with reference to FIGS. 1A to 1F. An oxide film 1 and a silicon layer 2 make contact with each other to construct a boundary B or an interface.
In the first case where mesh points on the boundary are treated as duplicated points, as illustrated in FIG. 1A, mesh points 3 are disposed in the oxide film 1 and the silicon layer 2 and on the boundary B therebetween. Upon formulating a diffusion equation, as illustrated in FIG. 1B, each mesh point on the boundary B is treated as a duplicated point, in which one point constituting the duplicated point is disposed inside the oxide film 1 with the other point being disposed inside the silicon layer 2.
In the second case where mesh points on the boundary are treated as duplicated points and the boundary protective layer is disposed, as illustrated in FIG. 1C, the boundary protective layer is set in the vicinity of the boundary B, and in the boundary protective layer the mesh is made dense. Then, the mesh points 3 are disposed in the oxide film 1 and the silicon layer 2 and on the boundary B. Upon formulating a diffusion equation, as illustrated in FIG. 1D, each mesh point 3 on the boundary B is treated as a duplicated point, and one point constituting the duplicated point is disposed inside the oxide film 1 with the other point disposed inside the silicon layer 2.
In the third case where mesh points on the boundary are treated as triplicated points, as illustrated in FIG. 1E, the mesh points 3 are disposed in the oxide film 1 and the silicon layer 2 and on the boundary B. Upon formulating a diffusion equation, as illustrated in FIG. 1F, each mesh point on the boundary B is treated as a triplicated point, and one point constituting the triplicated point is disposed inside the oxide film 1 with other one point disposed inside the silicon layer 2 and with a remaining one point left behind on the boundary as a mesh point 3 of an intermediate layer.
The aforementioned conventional method however suffers from a difficulty that, in the case where the boundary protective layer is not provided, a large control volume possessed by each mesh point on the boundary-causes migration of an impurity dose larger than the actual case together with effect that a transport coefficient of a segregation flux is very large, whereby the accuracy of simulation of a segregation phenomenon is severely deteriorated. In contrast, in the case where the boundary protective layer is provided, there is not yet established a general technique in which for an arbitrary three-dimensional device configuration the boundary protective layer is generated while maintaining Delauney partition in a three-dimensional structure where a plurality of substances are brought into contact, and hence there is not yet established a technique for generating the boundary protective layer without failure.
An object of the present invention is to provide a method for process simulation capable of simulating diffusion phenomena and impurity segregation phenomena while maintaining the accuracy of simulation without use of the boundary protective layer for a system including a substance boundary such as an interface between a silicon layer and an oxide film.
The above object is achieved by a method for process simulation for simulating a diffusion phenomenon in a system in which a first substance region and a second substance region make contact with each other to form a boundary, comprising the steps of dividing a device model of the system into a mesh to generate mesh points such that some of the mesh points are mesh points disposed also on the boundary; and formulating a diffusion equation by treating each mesh point on the boundary as a multiple point of quadruplicated or higher.
Here, the multiple point is a point in which a plurality of points are assembled. The assembled points are regarded and treated as a single point, that is the multiple point. The multiple point is, for example, a quadruplicated point (i.e., quadruple point), a quintuplicated point (i.e., quintuple point), or a sextuplicated point (i.e., sextuple point). In the case of the quadruplicated point, the diffusion equation may be formulated by distributing two points among four points constituting the quadruplicated points inside the first substance region with the remaining two points distributed inside the second substance region. In the case of the quintuplicated point, the diffusion equation may be formulated by distributing two points among five points constituting the quintuplicated point inside the first substance region with other two points distributed inside the second substance region and further with the remaining one point left behind on the boundary as an intermediate layer. In the case of the sextuplicated point, the diffusion equation may be formulated by distributing three points among six points constituting the sextuplicated point inside the first substance region with the remaining three points distributed inside the second substance region. In either case, upon formulating the diffusion equation a mutual interval of points constituting the multiple point is preferably enough smaller than the typical interval of a mesh, to be concrete a distance between adjacent points is preferably 0.3 nm or less.
In the present invention, as a combination of the first substance region and the second substance region there may be listed a combination of a silicon layer and an oxide film, for example.
In accordance with the present invention, there is no need of consciously forming the boundary protective layer when the mesh is generated, and simulation of a diffusion phenomenon, particularly segregation of any impurity is performed with maintaining predetermined accuracy of simulation. This is because any error caused by occurrence of parasitic thickness due to the multiple point construction can be restricted to a certain level or less by treating mesh points on the substance boundary in the diagrammatical arrangement of the device model as a multiple points of quadruplicated or higher, and setting an effective distance between adjacent points constituting the multiple point to be very short. The present invention is particularly effective in a three-dimensional process simulator where there is not established a technique to form without failure the boundary protective layer for a device of an arbitrary configuration in the present state.
The above and other objects, features and advantages of the-present invention will become apparently from the following description referring to the accompanying drawings which illustrate examples of the preferred embodiments of the present invention.